What happened
If Spawnable Prefab has "Local Player Authority" set and we do NetworkServer.SpawnWithClientAuthority():
1 On the host after NetworkServer.SpawnWithClientAuthority() it calls both OnStartAuthority and OnStopAuthority

2 when server and client are different instances -
OnStartAuthority() called on the client (correct)
OnStopAuthority() called on the server (wrong)

How we can reproduce it using the example you attached
1 Open attached project and open scene "scene 1"
2 Press Play
3 Press "LAN Host" (- cube should appear in the scene)
4 Press "Space" button on keyboard
Actual result: you will see 2 logs:
Object OnStopAuthority, hasAuthority = False
and
Object OnStartAuthority, hasAuthority = True
Expected result: only OnStartAuthority() should be called